The invention relates generally to electromagnetic amplification. In particular, the invention involves substrate dissipation and an array of dimers in which a “dimer” is defined as a structure formed from a complementary pair of similar sub-units. Each dimer is composed of one loss element and one gain element. The loss and gain elements have the same geometry and the same real part of the permittivity, but the opposite imaginary part of the permittivity.
In a pioneering work, Bender and colleagues proved that non-Hermitian Hamiltonian with parity-time () symmetry may exhibit entirely real spectrum below a phase transition (symmetry breaking) point. See C. M. Bender et al.: Real Spectra in Non-Hermitian Hamiltonians having PT Symmetry”, Phys Rev Lett 80 5243 (1998) and C. M. Bender et al.: “Complex Extension of Quantum Mechanics”, Phys Rev Lett 89 270401 (2002). Inspired by this emerging concept, in the past decade there has been a growing interest in studying -symmetric Hamiltonian in the framework of optics where the  complex potential in quantum mechanics is translated into a complex electrical permittivity profile satisfying ∈(r)=∈*(−r) in optical systems.
In optics, most of the -symmetric structures are realized by parallel waveguides or media with alternating gain and loss either along or across the propagation direction. The periodic spatial modulation of gain and loss in photonics and plasmonics structures has led to many intriguing phenomena such as nonreciprocal light propagation and invisibility, power oscillations, coherent perfect absorptions, loss-induced transparency, nonreciprocal Bloch oscillations, optical switching, unidirectional tunneling, loss-free negative refraction, and laser absorbers.
The -symmetric systems are a subset of open quantum systems for which the Hamiltonian is non-Hermitian, and the eigenvalues are complex in general. The unique properties associated with non-Hermitian Hamiltonian are exceptional points and spectral singularities, one being a branch point singularity associated with level repulsion and symmetry breaking. The existence of the exceptional point has been observed in microwave experiments. See S. Longhi: “Spectral singularities and Bragg scattering of complex crystals”, Phys Rev A 81 022102 (2010), and M. G. Moharam et al.: “Rigorous coupled-wave analysis of planar-grating diffraction”, J Opt. Sci Am 71 811 (1981). Spectral singularity is related to scattering resonance of non-Hermitian Hamiltonian and manifests itself as giant transmission and reflection with vanishing bandwidth. Exceptional points and spectral singularities possess interesting electromagnetic properties and have attracted much attention.